
We mention that \((\Lambda _{\varphi ,w})_a = (\Lambda _{\varphi ,w})_b\)  by the fact that \(\lim _{t \rightarrow 0+}\phi _{\Lambda _{\varphi , w}}(t) =\lim _{t \rightarrow 0+}\frac{1}{\varphi ^{-1}(1/W(t))} = 0\)  and by [1]}. For the sequence space, the relationship \((\lambda _{\varphi , w})_a = (\lambda _{\varphi , w})_b\)  always holds in view of [1]}. Notice that we have the Orlicz space \(L_{\varphi }\)  when \(w \equiv 1\)  and the Lorentz space \(\Lambda _{p, w}\)  for \(1 \le p < \infty \)  when \(\varphi (u) = u^p\) , \(u\ge 0\) .
